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Tyrrell_McAllister comments on Book Review: Naive Set Theory (MIRI research guide) - Less Wrong Discussion
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There is a convention according to which a one-to-one function is injective, while a one-to-one correspondence is an injective function that is also surjective, ie, a bijection. (I don't know whether Halmos uses this convention.)
Oh yes, for sure, but the context here was a statement that "onto" means surjective while "one-to-one" means bijective. Definitely talking functions. And I would be really surprised if Halmos were using "one-to-one" followed by anything other than "correspondence" to mean bijective.
You guys must be right. And wikipedia corroborates. I'll edit the post. Thanks.